The ability to reconstruct magnetic resonance (MR) images from vastly undersampled acquisitions has significant clinical value. It allows the duration of the MR scan to be reduced and enables the visualization of rapid hemodynamics.
Using advanced image reconstruction algorithms, images can be reconstructed with negligible loss in image quality despite high undersampling factors (R>6). To achieve this performance, algorithms exploit the data acquisition model with the localized sensitivity profiles of high-density receiver coil arrays for parallel imaging. Additionally, image sparsity can be exploited to constrain the reconstruction problem for compressed sensing. With the use of nonlinear sparsity priors, these types of reconstruction problems are solved using an iterative algorithm. These traditional iterative algorithms, however, have considerable computational complexity for undersampled data.
To improve the image reconstruction in terms of speed and robustness, deep convolutional neural networks (ConvNets) have been proposed. There are various challenges in applying ConvNets to MRI reconstruction, however.
ConvNets are conventionally trained and applied in the image domain. With the fundamental elements of the network as simple convolutions, convolutional neural networks are simple to train and fast to apply. In contrast, MRI data acquisition differs from conventional imaging applications because the data acquisition is performed in the frequency domain, or k-space domain. Consequently, many of the known techniques for image processing with ConvNets do not directly translate to MRI image reconstruction.
Existing ConvNets do not explicitly enforce that the reconstruction solution will not deviate from the measured data. Without a data consistency step, the ConvNets may “hallucinate” new structures in the image or remove existing ones, leading to erroneous diagnosis.
On the other hand, if an attempt is made to use a data consistency step, the training and application can not be image-patch based, because if only small image patches are used, known information in the measurement domain (k-space domain) is lost. As a result, the ConvNets must be applied and trained on fixed image sizes and resolutions. Thus, to train a ConvNet to accurately reconstruct a high-resolution MR image, the specific ConvNet must be trained on MR images with equivalent or higher spatial resolutions. This limitation increases the memory footprint of the ConvNet and decreases the speed of training and inference.
In addition, existing ConvNet techniques are not easily extendable to high-dimensional MR images and multi-dimensional MR images, because the training and inference of the ConvNet can never be fully parallelized: specific steps within the ConvNet (such as transforming from k-space domain to image domain) requires the gathering of all data before proceeding to the next step of the network.